Two-dimensional analysis of piezoelectric thin-film acoustic wave resonators

We derived a system of two-dimensional equations for thickness-extensional vibrations of a four-layered plate consisting of a piezoelectric thin film on an elastic substrate with driving and ground electrodes. It takes into consideration the couplings among the thickness-extensional mode to extensional, flexural, fundamental and second-order thickness-shear modes. Mindlin's approach of using a power series expansion of the displacement field in the plate thickness coordinate was employed. The propagation of straight-crested waves in the plate was studied. Furthermore, we used these equations to analyze FBAR's couplings vibrations, frequency spectra and mode shapes. It is shown that the equations obtained are very accurate for long waves in the plate. Free vibration results are helpful for the design of thin-film piezoelectric acoustic wave resonators to avoid the mode couplings.